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: http://www.apo.nmsu.edu/Telescopes/eng.papers/performance/performance1990.html
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We used a 0.3 m telescope attached to the telescope mount to monitor tracking and pointing performance. Currently, the telescope tracks open loop to 0.3 arc sec rms over 10 minutes and points to 5 arc sec rms. We expect that improvements to the servo system and encoder mounting will allow us to meet our goals of tracking to 0.2 arc sec rms and pointing to 1 arc sec rms.
The telescope is designed to acquire objects to within 1 arc sec rms, and to track open loop over a period of 10 minutes with an accuracy of 0.2 arc sec rms. Important features of the design include a fast (f/1.75) lightweight honeycomb mirror, a compact altitude/azimuth mount, friction-coupled drives and position encoders, and use of a telescope model to compensate for mechanical errors (1) .
As of February, 1990, the primary mirror is being polished. Currently, we measure the pointing and tracking accuracy of the mount using an intensified CCD camera attached to a 0.3 m telescope bolted to the mount altitude structure. Hence, effects such as flexure of the optics mounts and the effect of the instrument rotator are not included in the measurements reported here.
The telescope was designed to be mechanically stiff and accurate, but achieving the desired pointing accuracy requires correcting for remaining mechanical errors. To this end, we predict the error in azimuth and altitude as a function of the requested azimuth and altitude (and perhaps eventually other factors, such as temperature, or encoder pickoff wheel angle). This error function is called the telescope model. We use a physical model for our telescope, meaning that each term in the model describes some physical effect, such as tilt of the azimuth axis from the vertical. This is in contrast to an empirical model, in which the terms are chosen to be orthogonal, and do not represent physical phenomena.
Our present telescope model, consisting of ten terms, is shown in table 1 . The coefficients are determined by measuring pointing errors for a set of FK4 stars distributed fairly uniformly across the sky, and fitting the model to this data using the singular value decomposition least squares method. All terms except altitude drive disk runout (out-of-roundness) are generic, in that they apply to most altitude/azimuth mount telescopes. The altitude drive disk contains a high frequency ripple, making it difficult to model with standard terms. We tried using a set of independent altitude harmonics, but the high frequency coefficients were difficult to determine accurately. To solve this problem, we measured the disk's shape using an LVDT gauge head and generated a single pointing term using a 3rd-order harmonic series.
Coefficient Value Std. Dev. (arc sec) (arc sec) altitude zero point -132.5 2.9 azimuth zero point +90.6 7.6 azimuth axis tilt north -0.4 0.6 azimuth axis tilt west +1.7 0.6 non-perpendicularity of az/alt -52.9 8.5 altitude scale -199.3 3.4 altitude drive disk runout +12.5 1.5 non-perp of beam to alt axis +21.4 10.8 azimuth centering error, cosine +3.1 1.1 azimuth centering error, sine +11.9 1.1 rms error on the sky = 3.9 arc sec
We use TPOINT to generate and fit our telescope models. TPOINT was written by Patrick Wallace (3) . This program allows one to generate a variety of models, fit them to pointing data, and examine the residual error with many different graphs as an aid to refining the model. It comes with a large repertoire of physical and empirical pointing terms, and the user may add additional terms, such as our term for altitude drive disk runout. We have integrated TPOINT into the control system, so that any model we generate can be used to control the telescope. We expect this to prove useful for modelling the various instrument positions. For example, there are some pointing terms which apply only to Nasmyth foci.
Some pointing error is undoubtedly due to the encoder mountings. When we measure the positions of the absolute references using the incremental encoders, the results vary by one arc second in altitude and several arc seconds in azimuth. We believe this is caused by two factors. The gap between the absolute position reference magnets and the magnet sensing head apparently varies too much to give the required position repeatability. In addition, the incremental encoders are not well constrained to follow the drive disk, and we believe the resulting stresses are relieved by occasional slippage of the encoder. We are redesigning the mountings in an attempt to solve these problems.
We have also studied the axis controller's servo performance. The axis controllers record position errors over an interval of a few seconds, and we analyzed this data taken while moving the axes at various speeds. Over the range of tracking rates in altitude (0 to 0.004 deg/sec) we see rms errors up to 0.04 arc sec. In azimuth we tested speeds up to 1 deg/sec. Adjusting the error for altitude, we obtained rms errors on the sky of up to 0.2 arc sec. The worst azimuth errors occurred at speeds around 0.008 deg/sec; at higher speeds the cos(alt) factor more than compensates for increasing error. Our original error budget for each axis controller was 0.02 arc sec rms. Clearly we must improve the azimuth controller, but the altitude controller is probably acceptable. The servo errors in both axes are dominated by oscillations at 3 - 4 Hz and the servo loop operates at 20 Hz, so servo performance should be easy to improve.
Starlink Project
We would also like to thank Steward Observatory for the loan of their 0.3 m telescope.